## Using Multiple Moulding Widths In One Frame

Last updated on December 11th, 2019 at 11:49 am

In this article, the first of the “Weird Wood” seriesintro, we show how to build a picture frame using four strips of moulding that aren’t all the same width. Although Figure 1 uses a different width for each piece of moulding, we used three different sizes in our test frames (only because I couldn’t find four different sizes in the same moulding family).

## First The Math

Warning: This discussion includes a little trigonometry.  Do Not Panic! It’s not as bad as it sounds.

### Definition of “Tangent” (skip ahead To Next paragraph if you still remember this):

There are three sides to any right triangle (a triangle with a 90° corner), which I will call the height and the width, which both touch the right (90°) angle and the hypotenuse, which is opposite the right angle and is the triangle’s longest side. You can use the ratio of the lengths of any two of those sides to find the size of the other two angles. Each possible ratio has a name, but we are only interested in one of them today. Probably the most common ratio and the one we will be using is called the tangent. The tangent is defined as the ratio between the height (the length of the side opposite the angle you are interested in) and the width (the length of the shorter of the two sides that create that corner that you are interested in). If you want to know the angle of corner α in the above drawing (Figure 2), for instance, you would calculate its tangent by dividing the height (3 inches in this case) by the width (1¼ inches), which is 2.4 this time. Then you would use your calculator (or phone app – I use RealCalc Plus by Quartic Software (even though it cost 3.50)) to find the angle corresponding to that tangent. On your calculator, the tangent is abbreviated “tan”. If you enter 45 (degrees are assumed) and hit the “tan” button, you will get 1 because for a 45° angle the height is the same as the width, so their ratio is 1. To go the other way (to find the angle), like we are trying to do, we need the inverse of the tangent. Look for the “tan-1” button (it could be the same button, in which case you may need to hit a (yellow) shift or second-function key, and then hit the “tan” button). In this case, once we have the tangent of 2.4, we hit the inverse tangent button(s) to get 67.380135…. (the calculator is obligated to give you 8 or more digits – that doesn’t mean they mean anything. In Figure 2, I rounded that answer to 67.4 degrees and even that third digit should be suspicious.) ## The Process All you have to do is take the ratio between the widths of your two moulding pieces and take the inverse or arc-tangent to get the angle. Here are a few things you need to remember: 1. Which angle – the tangent gives you the angle that was touching the side whose length was used for the denominator (the width, which would be the second number in the division). The simplest way (but certainly not the only way) to get the other non-90° angle is to just subtract the first from 90° (since the two angles are complementary). Also remember that if the tangent was greater than one, the angle will be larger than 45°; if it was supposed to be a smaller angle (less than 45°), then you may have divided the two lengths in the ratio backward. Don’t worry, you just found the complementary angle and all you have to do to get the right answer is subtract what you got from 90. 2. It is up to you to keep track of whether that angle you are cutting should be to the left or the right. Making a drawing of your frame design might help. To be useful, the drawing doesn’t even need to be that good. This should also tell you if you calculated the complement (the other angle in that corner (for the other piece of moulding)). 3. Your saw may be measuring angle backward. My miter saw calls a cut perpendicular across the board 0°, not 90°. If that’s the case, just subtract the angle you calculated from 90. As an exercise, go ahead and check the rest of my calculations in Figure 1. 😁 ### Make The Cuts There is more than one way to make these cuts and more than one set of tools to help you. Which set of tools you should use will depend on such factors as how much of this work you intend to do, your skill set, what your budget is, and what tools you already have on hand. To see the Note click here.To hide the Note click here. Looking through the Framers’ Corner, the forum of the Professional Picture Framers Association, I found recommendations for the following tools for this application: 12-pc Precision Angle Block set (1/4, 1/2, 1 to 5, & 5 to 30 degree) You would only need one of these (if any), not both. (The Amazon.com descriptions are only used here as a reference. Although frequently competitive, Amazon isn’t always the only or the best place to buy something.) Our workshop includes all of the tools listed in www.BeeHappyGraphics.com/about.html#BruceEquip, along with a number of other regular hand & power woodworking tools that Nancy has accumulated over the last several decades. For this project, I used our compound miter saw, but not without complications. To see the Note click here.To hide the Note click here. The precision on this saw looked fine; you should be able to get within ¼° of your target. The first picture (Image A) shows me trying for 22.6° (which would be one of the angles between a 3″ and a 1¼” moulding). After cutting the 3″ piece, I ran into problems trying to cut the complementary angle (67.4°) on the 1¼” piece, as shown in Image B. I am not claiming that mine was the best path to reach our goal. In fact, I would love to see your ideas in the comment section about how to improve my techniques. #### How I Did It 1. Working with one corner at a time, I cut both pieces of moulding square just a tad longer than their overall/outside measurement according to your diagram (you will see why in Step 4). If you don’t already have one, this is also when you would put a perfectly square cut on the alignment block you’ll see in Figure 5 to the left of the moulding. I grabbed a 2″ by 4″, but the wider the better. 2. I set the saw for the smaller of the two complementary angles, rechecking my diagram to confirm whether it should be to the left or right. In the setup shown below, the 3″ moulding would be clamped to the right of the blade. 1. I made the cut. 1. Without adjusting the angle of the saw, I set up the second cut. I positioned my (newly cut) alignment block to the left (opposite the side we placed the moulding for the cut (in Step 2)) so that I could also place the 2″ moulding to the left of the blade and perpendicular (at a right (90°) angle) to the miter saw fence. After clamping down the alignment block, I added a support block to the right of the moulding to keep it in place. I could still move the moulding in or out to position the cut. You can see why I needed to precut this piece of moulding. 2. I made the cut. To see the Note click here.To hide the Note click here. For those who noticed that the color of the moulding in Figure 4 was different than in Figure 5, I had to make two different frames while doing research for this article 1) to confirm and refine my techniques and 2) because I didn’t get enough pictures the first time. 1. Always check your work. If, when you put the two pieces of moulding together, the miter edge on one piece is longer than the other, that is the angle that should have been larger. The angle on the other piece of moulding should have been smaller (by the same amount). Figure 7 shows the second setup from the right side. If you look close, you might notice that I didn’t cut enough to make a sharp corner and needed to recut. 1. Moving to the next corner, I precut at least one more piece of moulding and repeated Steps 2 through 6. 2. I repeated Step 7 two more times. The second time (when working on the last corner), I used the first two pieces of moulding I just finished cutting to mark the next cut by matching the inside edges, as shown in Figure 8. ### Finishing As with my normal (45° miter) frames, I would next need to make sure the inner lengths on opposite pieces of moulding matched, and the outer lengths as well. Figure 9 shows a way to check to see if the outside and inside corners of the opposite sides match using two carpenter squares (or equivalent). Some of the tools we normally use next to finish putting the frame together, namely our Logan Precision Sander and Logan Pro Joiner, are worthless for this application. After gluing (and clamping the pieces together until dry) we had to pound the V-nails in by hand (interestingly, the simpler Logan Studio Joiner can be adapted). ## The Back Side For completeness, the left figure below shows what the backside of the lower left corner would look like. The gray section represents the rabbet, the equal-width (¼”) cut-out that holds the glass, mats, image, and backing of the picture inside the frame. Some of you might be surprised to see that there is a triangular notch in this rabbet in the corner along the miter cut. This notch has no effect on the functionality of the rabbet. To solve this “problem”, however, you could make a compound cut 45° in from the inner edge to the edge of the rabbet and 79.7° in from the outer edge to the same point, as shown in the right figure below (as an exercise, you can check my math on these angles also). But there is really no need to make these cuts. If the gray were to represent an equal-width feature on the front of the moulding, it might be worthwhile to take the extra trouble. Otherwise, don’t even think about it. ## The End Congratulations, you now have a fancy new picture frame. Of course, you still need to find a picture, cut mat(s) and backing, mount picture to same, cut glass, assemble the pieces without showing any annoying little specks, and apply a dust cover and hanging hardware, but all of that is beyond the scope of this article. Good luck! As mentioned, this article is just the beginning of a series about “Weird Wood” that I announced months ago. Up next, we will look at handling moulding that is not of uniform width. You won’t find this moulding in any store; it is only an exercise to prepare you for our final project. But if it stimulates your creativity, that’s not always a bad thing. Stay tuned, and thanks for reading! Your comments are welcome and appreciated. ## All Rectangles Are Not The Same (or even Similar) Last updated on December 30th, 2019 at 09:03 pm Our friend, Ibis Hillencamp (whom you may remember for the advice she gave on our FAQ page about becoming a better photographerlink) thought people might need an explanation of a photograph’s aspect ratio and why you need to consider it when enlarging or cropping your images. After explaining that, I give some ideas for filling in additional space around your image that may result from changing the aspect ratio. When you enlarge a picture, unless you want distortion, you have to increase the width the exact same ratio as the height. For example, a 4″ by 6″ image might be enlarged into an 8″ by 12″ image, or a 10″ by 15″, and so forth. For each of these examples, the aspect ratio, which is the height divided by the width (or vice versa, as long as you are consistent), remains the same ($\frac{4}{6} = \frac{8}{12} = \frac{10}{15} = 0.66667$). Mathematicians would call the three rectangles in this example, and all others with the same aspect ratio, “similar”. When placed at the right distances, you would not be able to tell them apart. SLR cameras, starting with the analog 35mm and continuing to the digital versions, have an aspect ratio of 2:3 and can make prints the size of any of the above examples with no problem. Other cameras have different aspect ratios. If you haven’t already done so, learn your camera’s aspect ratio. ## And Now The Bad News The problem starts when you try to put your picture in a standard-sized frame. They routinely have a different aspect ratio. If you want an 8″ by 10″ print, for example, you will be changing the aspect ratio to 0.8. An 11″ by 14″ print has an aspect ratio of 0.786. The simple answer would be to crop your original image, which means you are going to lose part of the picture. That could be a problem. The other option is to fill in any missing parts. That is almost always a problem. Let me show you. For those of you who do not recognize her, the above picture is of my wife, Nancy, the nature and wildlife photographer (No, this is not a selfie). This image has an aspect ratio of 4:3. Suppose we want to put her picture in a mat with a 3:2 aspect ratio. The easiest thing would be to crop to the red rectangle, which is the largest such rectangle we can get from the given material. But as you can see, there is no breathing space around the hat. So we could enlarge to the orange rectangle to use the original picture’s entire width, but we will need to get creative and fill in some along the top and bottom edges (by the way, can you guess why the top and bottom voids created by the orange rectangle are not the same size?). While the techniques to fill those voids are beyond the scope of this article, I would like to share a few thoughts. These thoughts apply not only to the case where you need to add material to change aspect ratio but for other causes also, like when you inadvertently cut off some body part when taking the shot. ## Suggestions For Filling Missing Space • The first moral to this dilemma is don’t get too tight on your subject while shooting. Start leaving yourself a little more edge room when you take your pictures. Besides not inadvertently cutting off parts of the subject, which are harder to bring back after-the-fact, you might actually capture the subject’s whole reflection, which you didn’t even notice in the excitement of getting this unique subject. • The first step in processing this change in aspect ratio is to go back and check the original file. Maybe you had previously cropped the image for compositional purposes and the original might still have at least part of the now-missing material that you need. • Small, uncomplicated additions are easy enough with Photoshop’s Clone Stamp tool (and although I’m not a huge fan, sometimes Content-Aware Fill might even work), but it gets trickier as the size of the addition increases. It would be no problem to fill the new space above Nancy’s head with sky, and maybe even throw in an extra cloud or two, but if for some reason, we had wanted to extend the left edge of this image an inch or so, finding enough water to fill the gap without people noticing repetitions could be an issue. • Sometimes you can create more usable material from within the image itself by copying some of the waves, for example, and flipping them, or rotating them, etc. But you will have to judge the effectiveness of these actions on a case-by-case basis. • Look at the photograph you took just before this one and just after this one for more material. Especially if you are shooting wildlife, I know you had your camera on rapid-shoot. The neighboring shot that you didn’t select for this image may have ‘new’ material that would be useful for your current extension project. • Continue to expand your search area. Even if you didn’t get another picture of your subject squirrel that day, you might have other squirrel pictures you can use to replace that missing piece. ## Send Your Ideas Well, that’s all I have for now. Although I have no intentions yet of following this article with more detailed information on the Clone Stamp or other tools, I am pretty sure there are plenty of tutorials out there, both by Adobe and by several third parties. If you do have your own hard-earned techniques or suggestions on any of the material I’ve just discussed or even a horror story that’s relevant, I’m sure my readers would love to see your comments below. Thanks. ## Tell It To The Judge: In Defense Of Photographers & Canvas Last updated on November 18th, 2019 at 06:38 pm To be transparent, I must say I’ve developed some theories about the biases of art critics and the judges of art festivals, based mostly on their selections of art to be awarded prizes at these festivals (and maybe my own biases). I’ve noticed certain patterns that I was hesitant to discuss here until I had taken the time to formally learn something about art. That hasn’t happened yet, but we did have an opportunity to discuss photography (more specifically, nature and wildlife photography) with the judges at one recent art festival and I feel compelled to address one aspect of that discussion. My comments on the other aspects may wait until I satisfy my original goals/requirements. Today’s comments involve canvas. ## The Judges’ Remarks One of the judges said, “I’ve Never Seen A Photograph On Canvas That I Like”. There were three judges at the table when Nancy approached them. Their views were all consistent. Other remarks included “When I see a photograph on canvas I think the photographer is trying to impersonate a painter” and ‘When I see a picture wrapped around the edge of the canvas, it makes me think they are adapting a larger picture to a frame that is too small.’ One judge pointed out that painters don’t paint the side of their canvas. ## Our History Those familiar with our website know there are already two places where I’ve referred to painters as pre-photographers: You also know I’ve even chided fellow photographers for not keeping up with the times Stop Thinking Like A Film Photographer!. ## A Dose of Reality Painters like Leonardo di ser Piero da Vinci (1452-1519) and Georges Seurat (1859-1891) (see the first note in “A Question About Pixels”) are just two examples of artists who led society into the future, not followed. I’m sure if Leonardo had a camera, he would have used it in a flash (forgive the pun, I couldn’t help myself). These two and their peers would be saddened (or worse) to think that painters now feel unable to keep up with society and judges feel a need to artificially reserve materials and techniques specifically for painters in an effort to level the playing field. ## My Responses Now I’d like to address some of their remarks individually. “When I see a photograph on canvas I think the photographer is trying to impersonate a painter” A few months before this conversation, a painter at another prominent festival in Florida won Best Of Show and10,000 for impersonating a photographer. I know another artist who uses pencil to imitate black & white photographs. This is called realism, which apparently artists have tried (with varying degrees of success) throughout history, most notably in the Realist Movement of the mid-nineteenth century.

So here’s a question: if canvas-using photographers are impersonating painters, who was Leonardo impersonating when he painted the two versions of Virgin of the Rocks in oils on wooden panels? A sculptor, maybe? Maybe a carpenter like the protagonist in his famous mural
“The Last Supper”? Or maybe that particular impersonation has been reserved for the judges.

“When I see a picture wrapped around the edge of the canvas, it makes me think they are adapting a larger picture to a frame that is too small.”

Well maybe that’s why painters do it. After all, contrary to the one judge’s declaration, some painters do paint the sides. But have you ever see a painter warp the image around the edge so that at some angle it creates an illusion and looks like a continuation of the front image (as described in the Canvas section of our Services page)? While we are at it, have you ever seen a painter camouflage their signature to make it less distracting (which solves a problem some critics have complained to photographers about)? Here’s how we do it ( Our New Technique For Signatures & Titles). Come on, painters, try to keep up!

“I’ve Never Seen A Photograph On Canvas That I Like”

I recently heard from another wildlife photographer about a time when a judge took a liking to one of her images, but then left without comment. When the judge came back the second time, he asked if she had another copy of that image that wasn’t printed on canvas. Fortunately, she did, because that second copy won her the second-highest award in the festival.

In our booth and online, I’ve discussed the magical properties of canvas. When people see one of Nancy’s images on canvas they are more likely to ask “Is this a painting?’ or are more likely to comment that it looks three-dimensional. For some strange reason, it is also perfectly acceptable to print a particular photograph larger on canvas.

People have offered a couple of explanations for this. The first argues that the texture of the canvas disguises any lack of resolution. The second, getting psychological, suggests that canvas invokes some painting mentality, making the viewer less critical (nobody ever asked an eighteenth-century master how many pixels were in his/her brush). Both explanations sound plausible to me, but being a pragmatist, I just run with what works.

So it is especially disturbing, and sad, that a judge would make a statement like this. Photographers follow the same rules of composition and the same principles of art, but for a judge to admit that these are not important, to me is an admission that the judges don’t really know what makes a piece of art special and are just grasping at fads or straws.

At least that’s how I see it (I guess now is a good time to remind you that the views expressed in this blog are not necessarily those of management). So what’s your view. If any of you can make better sense of these judges’ remarks, your comments are also welcome.

## Thoughts On Mat Layout

The easiest and most common mat layout is one with the widths of all four borders equal. If you are forcing a picture into a standard-sized frame, however, that’s not always possible. And then there’s the matter of bottom-weighted mats.

### Bottom-Weighted Mats

Bottom-weighted mats, or mats with the bottom edge wider than the others, were introduced long, long ago. Some say that pictures centuries ago were hung very high on the wall and the bottom width of the mat was increased to compensate for the ‘distortion’ of that perspective. Unfortunately, that story makes no sense; top-weighting would be required to correct for the top being further from the viewer than the bottom. Another explanation involves the notion of a difference between the visual or optical center and the geometric center. Yet others claim it is to compensate for the drop of the mat in the frame due to tolerances necessary to account for expansion, etc. For whatever reason, bottom weighting could be seen as an attempt to fool your audience or overcome optical perceptions, whichever you prefer. As commonly practiced in “finer frame shops everywhere”, the bottom width is generally increased ¼” to 1″, depending on the size of the pictureref.

### Using Standard Mats

But how would one incorporate bottom weighting while fitting an image into a standard-sized mat? For example, if the vertical difference between the hole size and mat size is greater than the horizontal difference, and assuming the left and right borders will be the same width, is it better to:

 A Make the top and bottom borders equal, B Make the top the same size as the left and the right and put all of the extra width on the bottom, C Make the bottom larger than the top by some fixed amount, D Make the differences even more subtle by making the difference between the top border and the side borders the same as the difference between the top and bottom borders?

Let’s clarify your choices with an example. Suppose you want a 4″-high hole that’s 7″ wide in a standard 8″-high by 10″ mat. The horizontal difference between the mat size and the hole size is 10″ – 7″ = 3″, so if you want the left and right borders to be the same, each will be 3″ ÷ 2 = 1½”. The vertical difference between mat and hole size is 8″ – 4″ = 4″.

 Choice A Would make the top and bottom borders the same, making them each 4″ ÷ 2 = 2″. Choice B Would make the top 1½” like the left and right borders, leaving 4″ – 1½” = 2½” for the bottom border. Choice C Uses the customary bottom weighting, which the one reference I give above lists as ¼” for an 8″x10″ mat (personally, a ¼” bottom weight isn’t worth the trouble). That means the top border would be (4″ – ¼”) ÷ 2 = 1⅞” and the bottom would be ¼” more, or 2⅛” (notice as you check your work that 1⅞” + 2⅛” = 4″). Finally, Choice D Is a tad more complicated. Let’s call the difference between the left or right border width and the top border width “d”, such that 1½” + d = T (for top border width). Then the bottom border (B) would be T + d or (substituting the last expression for T) (1½” + d) + d = 1½” + 2⋅d. Since T + B = 4″, then (substituting for T and B) (1½” + d) + (1½” + 2⋅d) = 4″, meaning 3″ + 3⋅d = 4″ or 3⋅d = 1″, meaning d = ⅓”, so (substituting back into our equations for T and B) T = 1½” + ⅓” = 15/6” and B =15/6” + ⅓” = 21/6” (again noting that 15/6” + 21/6” = 4″) .

The choice you make would be an artistic decision, but I think A is the most common answer. Choice C could be used for traditional bottom-weighting, as in our example, or could be used for some other more artistic value. Technically, both Choices B and D are possible results of that equation. B would be exactly what you get when you want bottom-weighting and are not restricted to standard mats; it would work best if the resulting difference between the top and bottom borders is not too much greater than the customary bottom-weighting distances mentioned above. In our example, it yields 2½” for the bottom border, which is an inch larger than the other three borders and may just be too much.  In our example, C and D are very close, and remain close when we change the amount of weight in C from ¼” to ½” (as shown by the lighter blue opening).  D is more subtle than C, but may only be worth the effort when the difference between the left and top borders is small enough to fool somebody.  In other cases with different numbers, results may vary.

### With Larger Side Borders

If the horizontal difference between the hole size and the mat size is greater than the vertical difference, you could face up to the same number of choices as above, but you are working with less material for the top and bottom borders and I think it is usually better to keep things simple and make those borders equal.

### Differing Left And Right Borders?

Do the vertical borders always need be the same size? Although I can’t say I’ve ever seen or read about different-sized side borders, I’m not convinced that uniformity is strictly required. For example, in photography, as in older art forms, there a “rule” of spaceref that says, among other things, that there should be plenty of space on the side of the subject into which it is looking. If you have a “perfectly” centered and close-cropped picture of your mother looking to your left, could a mat with a wider border on the left side create the space that’s lacking in the image?  Maybe you could even choose a mat color that is a pastel version of the background to her right (your left)? Maybe a contrasting outer mat could be added with traditional (identical) vertical borders.

I present the above thoughts to give some background and (more importantly) stimulate your own creativity. If you think of other possibilities, I’d be thrilled to have you add them to the comments. Thank you!

## Working With Weird Wood: Preface

A few years ago, Nancy took a photograph of her junior-high-school best friend JoAnne’s father on a tractor at his northern-Florida homestead and gave it to JoAnne. After he died, JoAnne brought the picture back, along with some of the old fence pickets from the property, and asked if we could use them to frame the picture. After a lot of research, planning, and experimentation, this is what we came up with:

The pickets were thin, dilapidated, warped, and dirty. The few articles I did find were about “barn wood” which, although it had a slightly distressed surface, was still thick and sound with straight, flat, parallel and perpendicular sides – none of which applied here. The articles were not all that helpful and not all that well written. I thought this project could be an opportunity to learn something new, and to share it with you. I hope I took enough notes and pictures to show you exactly how this frame was made. At least that’s the plan.

### But First . . .

From math class, you may remember that one problem-solving strategy is to solve a simpler problem first and then use that answer to help solve the harder problem.  With that in mind, I have an idea to write a series of short articles on working with weird wood to make frames, so that I can draw on that information in the final article about this project.  The first article will be about working with pieces of moulding of different widths in the same frame.  Then I see a discussion of moulding where the inside and outside edges are not parallel.  Maybe then we’ll work with wood with a wavy inside edge.  Following that may be a discussion about what to do when your moulding is curved (but with uniform width).  But even before the first article, I may have to give a short post about matting techniques.  My hope is that by doing all of this it will expand your view of what’s possible and it will stimulate those creative juices of yours.  These articles will probably not be consecutive blog posts; another art festival season has just begun and other things will invariably come up as I am writing these pieces.  So please be patient and stay tuned.  Thank you!

## How We Digitally Stretch Our Gallery Wrap Edges Before Printing

As we discussed on the Services page of our website, we digitally “stretch” our image before wrapping it around the edge of our gallery-wrapped canvas images. Here’s how we do that:

Our gallery wraps are either 3/4” thick or 11/2“. On the thin ones, I usually take the 1/4” strip along the edges and stretch it to 1″, thus having an extra 1/4” to wrap around to the back side to cover for variations in the printing and stretching processes. On the larger ones, I take 1/2” and stretch it to 2″ (thus leaving 1/2” on the back). I wouldn’t stretch the image more than four times its original size, but you could go less. To do that, you would effectively be taking a wider margin to wrap around the side.

As an example, if I want a 12” x 18” image stretched around a 11/2” frame, I would crop the image to 13” x 19”. Then, after putting guides 1/2” in from each edge and another guide right on each edge, I would increase the canvas size 3” in both dimensions to get 16” x 22” with the image centered.

1. Click Image ⇨ Canvas Size…
2. Put a check in the Relative Box
3. Make Width and Height 3 Inches
4. Make sure Anchor dot is in center of the grid
5. Hit OK

I would then use a scale transform to digitally stretch the outermost 1/2” to 2” wide, filling the canvas.

1. Make sure Snap is checked in the View Menu
2. Use Rectangular Marquee tool to select the 1/2” strip between the guides along one of the edges
3. Click Edit ⇨ Transform ⇨ Scale
4. Place the mouse cursor over the little square in the middle of the outer edge of the selected area and drag to the edge of the canvas
5. Hit the check mark to finish the transform
6. Repeat Steps 2 through 5 with the 1/2” strips along the other three edges

(Actually, I first do the four corner squares separately, but since only a small bit along the edge of those squares has any chance of being seen, you could include them in either the horizontal or vertical strips (or even both)).

Then I add a blank (transparent) edge around the image representing the canvas I need for stretching the canvas around the frame by increasing the canvas size by double the required margins in both dimensions, the same way we did above. That margin would be at least the width of the moulding along the bottom (1″ for the 11/2” moulding we are using now) and enough extra to get a grip with the canvas pliers (for me that’s at least 3/4“). That would make the image’s final dimensions at least 191/2” x 251/2“. When I am finished, I add layers with cut lines, fold lines, staple lines, positioning marks for the hanging hardware, etcetera, but that is a personal matter beyond the scope of this article.

## A Solution To Second Mat(h) Problem

Last updated on November 16th, 2017 at 08:13 am

Sadly, we had no winners to this contest. Here is a solution to that math problem:

There is more than one way to solve this problem, but we will be exploiting three different relationships. First, in preserving the aspect ratio, the length of the image (we’ll call L) is 11/2 times the width (W). $L = 1.5W$. Then, adding up the components making up the overall width of the mat, the image width (less two overlaps of 1/8“) plus two mat widths (M) would equal 16 inches. $W - \frac{1}{4}" + 2M = 16"$ By the same token, the image length (less same overlaps) plus two mat widths would be 20 inches. $L - \frac{1}{4}" + 2M = 20"$

If you replace the L in the last equation with its W equivalent from the first equation, and then add 1/4” to both sides of both equations to combine constants, you are left with the following two equations to solve with two unknown variables:

$\begin{array}{r c l} 1.5W & + 2M = & 20.25 \\ W & + 2M = & 16.25 \end{array}$

From here you can use linear algebra (matrices) or algebraic manipulation to simplify until you are left with just one variable. For example, just subtracting the bottom equation from the top (subtracting the left sides separately from the right sides of each equation), you will wind up with

$0.5W = 4$

which means the image width is eight inches, which means its length is twelve inches, and the mat guide would be set to 41/8“.

### What’s Next

I’ve come up with one more printing-inspired math problem, which I will share as soon as I master a new plug-in for this blog.  After that, I’m not sure.  Response has been weak, but the former teacher in me feels a need to keep pointing out opportunities to use some of this stuff you learned in school (or is it just to torment those students who were the most difficult – I’m not telling).  This isn’t really costing anything, and I give enough warning for the math-averse to stay clear.  Stay tuned.